A universal law for non-breaking surface wave decay

Macroscopic friction can emerge from microscopic fluctuations whose mean vanishes but whose autocorrelation does not. Here we use this statistical-mechanical route to resolve a sixty-year-old problem in ocean wave physics, how non-breaking surface waves lose energy to upper-ocean turbulence. The Navier-Stokes equations contain a stochastic vortex force (the coupling between wave orbital motion and turbulent vorticity fluctuations) that classical wave-current theory discards because its phase average is zero. Yet its finite-time autocorrelation survives, yielding a non-negative Green-Kubo transport coefficient and, with inertial-range scaling, a parameter-free decay law determined by the turbulent dissipation rate, wave frequency and gravity. Remote ocean swell, where competing processes are weak, isolates this mechanism for direct test. The same framework predicts two observational signatures that previous analyses missed. The standard satellite estimator systematically exceeds the physical decay rate because of an Ito correction, and a substantial fraction of individual tracks must display apparent energy gain. These events are not merely outliers or measurement artefacts, but the most discriminating fingerprint of the stochastic theory. Both predictions are supported by global satellite observations. Our results reveal a hidden non-breaking pathway by which upper-ocean turbulence drains wave energy into the ocean interior, and show how macroscopic dissipation can emerge from fluctuations that deterministic averaging eliminates.